To create a valid data frame consisting of ImPACT scores, PCSS scores, and RTL/RTP information from the SIMS data set, the following steps were taken:
onset_rtl_total_daysrtl_rtp_total_daysonset_rtp_total_daysdays_between_injury_test_date) to quantify the duration of time between the onset date (SIMS data set) and the test date (ImPACT data set). Injuries were kept in the data set if the duration of time from onset to test date was between 0-30 days. With injuries outside this range removed, the new data set to be used for analysis consists of 208 injuries.To calculate the duration of time from injury onset (onset) and ImPACT test date where PCSS scores were collected (test_date), a variable was created (days_between_injury_test_date) to represent this duration of time. Injuries where testing occurred more than 30 days after the injury were removed from the data set.
Using Lumba-Brown et al. (2019) and Harmon et al. (2019) as references, the 22 PCSS symptoms were organized into the following six symptom clusters:
PCSS Total Possible Score: 132
## [1] 0.1571708
## [1] 0.1166308
## [1] 0.1774048
## [1] 0.130307
## [1] 0.2200165
## [1] 0.1305177
## [1] 0.09691213
Extreme outliers exist for all predictor and outcome variables, where predictor variables correspond to the PCSS total symptom and cluster scores, and the outcome variables correspond to the duration of time to complete the RTL and RTP process.
Linear model of the relationship between total PCSS symptom score and the duration of time to complete RTP protocol
Model strengths:
Model weakness:
Overall Interpretation:
There does appear to be a relationship between PCSS total symptom score and the duration of time to complete the RTP protocol; however, the model is weakened by the presence of outliers and high level of variance in both the predictor (total PCSS score) and outcome variable (RTP completion time).
##
## Call:
## lm(formula = onset_rtp_total_days ~ total_symptom_score, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.867 -11.907 -7.037 1.702 254.352
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.0367 2.6431 8.337 1.08e-14 ***
## total_symptom_score 0.3479 0.1523 2.284 0.0234 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.43 on 206 degrees of freedom
## Multiple R-squared: 0.0247, Adjusted R-squared: 0.01997
## F-statistic: 5.218 on 1 and 206 DF, p-value: 0.02338
Multiple regression model where gender has been added as a predictor variable.
Model Strength:
Model Weakness:
##
## Call:
## lm(formula = onset_rtp_total_days ~ total_symptom_score + gender,
## data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26.627 -11.773 -6.724 2.016 253.048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.4941 4.1929 5.842 2e-08 ***
## total_symptom_score 0.3204 0.1567 2.044 0.0422 *
## genderMale -3.5005 4.6332 -0.756 0.4508
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.47 on 205 degrees of freedom
## Multiple R-squared: 0.02741, Adjusted R-squared: 0.01792
## F-statistic: 2.889 on 2 and 205 DF, p-value: 0.05791
Multiple regression model where age has been added as a predictor variable.
Model Strength:
Model Weakness:
##
## Call:
## lm(formula = onset_rtp_total_days ~ total_symptom_score + age,
## data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.592 -12.114 -6.381 1.108 250.886
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15.3843 31.5545 0.488 0.6264
## total_symptom_score 0.3270 0.1553 2.105 0.0365 *
## age14 10.9972 31.8512 0.345 0.7303
## age15 10.6091 31.7837 0.334 0.7389
## age16 1.9603 31.8970 0.061 0.9511
## age17 2.5744 31.9241 0.081 0.9358
## age18 2.6583 32.8377 0.081 0.9356
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.53 on 201 degrees of freedom
## Multiple R-squared: 0.04258, Adjusted R-squared: 0.014
## F-statistic: 1.49 on 6 and 201 DF, p-value: 0.1832
The total symptom score model has the lowest AIC value (as indicated by the “delta” value), suggested it is the strongest model of the three compared. Lower AIC values indicate stronger model fit.
## predictors delta weight
## 1 total_symptom_score 0.000000 0.59
## 2 total_symptom_score + gender 1.421620 0.29
## 4 gender 3.619591 0.10
## 3 total_symptom_score + age 6.151670 0.03
Linear model between the headache-migraine symptoms cluster score and duration of time to complete RTP protocol. The headache-migraine coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtp_total_days ~ headache_migraine, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.596 -12.360 -7.662 0.778 258.843
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.6616 2.7469 8.250 1.87e-14 ***
## headache_migraine 1.1869 0.7042 1.685 0.0934 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.61 on 206 degrees of freedom
## Multiple R-squared: 0.0136, Adjusted R-squared: 0.008814
## F-statistic: 2.841 on 1 and 206 DF, p-value: 0.09341
Linear model between the cognitive symptoms cluster score and duration of time to complete RTP protocol. The cognitive coefficient is significant, suggesting there is evidence for a slight relationship between cognitive symptom severity and RTP completion duration. However, it should be stated that this model accounts for very little variance as indicated by the R-squared and Adjusted R-squared values.
##
## Call:
## lm(formula = onset_rtp_total_days ~ cognitive, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.789 -11.084 -7.051 1.949 255.080
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.0514 2.5387 8.686 1.16e-15 ***
## cognitive 1.5410 0.5956 2.587 0.0104 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.33 on 206 degrees of freedom
## Multiple R-squared: 0.03147, Adjusted R-squared: 0.02677
## F-statistic: 6.694 on 1 and 206 DF, p-value: 0.01036
Linear model between the anxiety-mood symptoms cluster score and duration of time to complete RTP protocol. The anxiety-mood coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtp_total_days ~ anxiety_mood, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30.921 -11.576 -6.694 1.541 257.250
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.4587 2.4300 9.654 <2e-16 ***
## anxiety_mood 1.4701 0.7794 1.886 0.0607 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.56 on 206 degrees of freedom
## Multiple R-squared: 0.01698, Adjusted R-squared: 0.01221
## F-statistic: 3.558 on 1 and 206 DF, p-value: 0.06066
Linear model between the ocular-motor symptoms cluster score and duration of time to complete RTP protocol. The ocular-motor coefficient is significant, suggesting there is evidence for a slight relationship between ocular-motor symptom severity and RTP completion duration. However, it should be stated that this model accounts for very little variance as indicated by the R-squared and Adjusted R-squared values. I also wonder how sensitive this model is as the ocular-motor cluster corresponds to only one symptom, while the other clusters correspond to 3-5 symptoms.
##
## Call:
## lm(formula = onset_rtp_total_days ~ ocular_motor, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.860 -10.433 -6.183 1.067 251.258
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.183 2.264 10.239 < 2e-16 ***
## ocular_motor 8.280 2.558 3.237 0.00141 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.05 on 206 degrees of freedom
## Multiple R-squared: 0.04841, Adjusted R-squared: 0.04379
## F-statistic: 10.48 on 1 and 206 DF, p-value: 0.001407
Linear model between the vestibular symptoms cluster score and duration of time to complete RTP protocol. The vestibular coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtp_total_days ~ vestibular, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.715 -11.490 -7.384 0.767 253.588
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.2325 2.4835 9.355 <2e-16 ***
## vestibular 1.5755 0.8339 1.889 0.0602 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.56 on 206 degrees of freedom
## Multiple R-squared: 0.01703, Adjusted R-squared: 0.01226
## F-statistic: 3.57 on 1 and 206 DF, p-value: 0.06024
Linear model between the sleep symptoms cluster score and duration of time to complete RTP protocol. The sleep coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtp_total_days ~ sleep, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.587 -12.017 -6.901 1.459 261.436
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.5408 2.5875 9.098 <2e-16 ***
## sleep 0.8604 0.6157 1.398 0.164
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.68 on 206 degrees of freedom
## Multiple R-squared: 0.009392, Adjusted R-squared: 0.004583
## F-statistic: 1.953 on 1 and 206 DF, p-value: 0.1638
The relationship between the cognitive symptom cluster and ocular-motor symptom cluster was analyzed with a multiple regression model. The results of the model reduced the cognitive coefficient to non-significance, while the ocular-motor coefficient remained slightly significant. As with the previous models, the amount of variance accounted by the model continues to be low.
##
## Call:
## lm(formula = onset_rtp_total_days ~ cognitive + ocular_motor,
## data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.445 -10.368 -6.368 1.632 250.094
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.3677 2.5240 8.862 3.81e-16 ***
## cognitive 0.5588 0.7610 0.734 0.4636
## ocular_motor 6.7544 3.2970 2.049 0.0418 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.08 on 205 degrees of freedom
## Multiple R-squared: 0.0509, Adjusted R-squared: 0.04164
## F-statistic: 5.497 on 2 and 205 DF, p-value: 0.004724
The ocular motor model is the strongest model, but there could possibly be a case to include cognition in a multiple regression model. Overall, these two symptom clusters appear to be the strongest predictors of RTP duration, but all models are limited due the low R and Adjusted R values. This is likely due to a smaller sample size, variance in predictor and outcome variables, and the presence of outliers.
## predictors delta weight
## 2 ocular_motor 0.000000 0.61
## 3 cognitive + ocular_motor 1.453572 0.29
## 1 cognitive 3.669073 0.10
## [1] 0.07304613
## [1] 0.02707833
## [1] 0.109808
## [1] 0.08910868
## [1] -0.02879951
## [1] -0.007090639
## [1] 0.09902616
Extreme outliers present.
Linear model of the relationship between total PCSS symptom score and the duration of time to complete RTL protocol. The coefficient of PCSS total symptom score is not significant, suggesting there is not a relationship between total PCSS symptom severity and duration of time to RTL.
##
## Call:
## lm(formula = onset_rtl_total_days ~ total_symptom_score, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6334 -3.0252 -1.5735 0.7311 22.9504
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.02521 0.40228 10.006 <2e-16 ***
## total_symptom_score 0.02437 0.02318 1.051 0.294
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.784 on 206 degrees of freedom
## Multiple R-squared: 0.005336, Adjusted R-squared: 0.0005073
## F-statistic: 1.105 on 1 and 206 DF, p-value: 0.2944
Linear regression model between gender and duration of time to complete RTL. The gender coefficient is not significant, suggesting the model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ gender, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9744 -2.8385 -1.8385 0.1615 22.0256
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.9744 0.5395 9.220 <2e-16 ***
## genderMale -1.1359 0.6825 -1.664 0.0976 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.765 on 206 degrees of freedom
## Multiple R-squared: 0.01327, Adjusted R-squared: 0.008479
## F-statistic: 2.77 on 1 and 206 DF, p-value: 0.09756
Linear regression model between age and duration of time to complete RTL. The age coefficient is not significant, suggesting the model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ age, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.064 -3.061 -1.525 0.814 21.936
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.000 4.794 0.626 0.532
## age14 1.061 4.843 0.219 0.827
## age15 2.063 4.832 0.427 0.670
## age16 0.186 4.850 0.038 0.969
## age17 1.525 4.854 0.314 0.754
## age18 1.000 4.990 0.200 0.841
##
## Residual standard error: 4.794 on 202 degrees of freedom
## Multiple R-squared: 0.02055, Adjusted R-squared: -0.003696
## F-statistic: 0.8476 on 5 and 202 DF, p-value: 0.5175
Multiple regression model with PCSS total symptom score and gender as predictor variables. Neither coefficient is significant, suggesting the model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ total_symptom_score + gender,
## data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0543 -2.7462 -1.7201 0.2676 22.2396
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.74402 0.63575 7.462 2.38e-12 ***
## total_symptom_score 0.01633 0.02376 0.687 0.493
## genderMale -1.02391 0.70251 -1.458 0.147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.771 on 205 degrees of freedom
## Multiple R-squared: 0.01554, Adjusted R-squared: 0.005933
## F-statistic: 1.618 on 2 and 205 DF, p-value: 0.2009
Multiple regression model with PCSS total symptom score and age as predictor variables. Neither coefficient is significant, suggesting the model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ total_symptom_score + age,
## data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3875 -2.8740 -1.7802 0.6497 22.1288
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.85248 4.80269 0.594 0.553
## total_symptom_score 0.01844 0.02364 0.780 0.436
## age14 1.02999 4.84785 0.212 0.832
## age15 2.00027 4.83758 0.413 0.680
## age16 0.23365 4.85483 0.048 0.962
## age17 1.47844 4.85895 0.304 0.761
## age18 0.86324 4.99799 0.173 0.863
##
## Residual standard error: 4.799 on 201 degrees of freedom
## Multiple R-squared: 0.0235, Adjusted R-squared: -0.005645
## F-statistic: 0.8063 on 6 and 201 DF, p-value: 0.5661
The gender model has the lowest AIC value (as indicated by the “delta” value), suggested it is the strongest model of the five compared. Lower AIC values indicate stronger model fit. However, none of the individal models are significant, likely due to the large amount of variance in the outcome variable (RTL duration).
## predictors delta weight
## 2 gender 0.000000 0.51
## 4 total_symptom_score + gender 1.521277 0.24
## 1 total_symptom_score 1.665586 0.22
## 3 age 6.459847 0.02
## 5 total_symptom_score + age 7.831214 0.01
Linear model between the headache-migraine symptoms cluster score and duration of time to complete RTL protocol. The headache-migraine coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ headache_migraine, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4990 -3.1668 -1.3537 0.6256 22.7917
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.16679 0.41667 10.000 <2e-16 ***
## headache_migraine 0.04153 0.10682 0.389 0.698
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.795 on 206 degrees of freedom
## Multiple R-squared: 0.0007332, Adjusted R-squared: -0.004118
## F-statistic: 0.1512 on 1 and 206 DF, p-value: 0.6978
Linear model between the cognitive symptoms cluster score and duration of time to complete RTL protocol. The cognitive coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ cognitive, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8160 -2.9472 -1.9472 0.4012 23.0528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.94720 0.38642 10.215 <2e-16 ***
## cognitive 0.14375 0.09066 1.586 0.114
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.768 on 206 degrees of freedom
## Multiple R-squared: 0.01206, Adjusted R-squared: 0.007262
## F-statistic: 2.514 on 1 and 206 DF, p-value: 0.1144
Linear model between the anxiety-mood symptoms cluster score and duration of time to complete RTL protocol. The anxiety-mood coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ anxiety_mood, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7862 -3.0590 -1.3620 0.6607 22.9410
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.0590 0.3679 11.033 <2e-16 ***
## anxiety_mood 0.1515 0.1180 1.284 0.201
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.778 on 206 degrees of freedom
## Multiple R-squared: 0.00794, Adjusted R-squared: 0.003125
## F-statistic: 1.649 on 1 and 206 DF, p-value: 0.2006
Linear model between the ocular-motor symptoms cluster score and duration of time to complete RTL protocol. The ocular-motor coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ ocular_motor, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3092 -2.4517 -1.3092 0.6908 22.6908
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.3092 0.3497 12.324 <2e-16 ***
## ocular_motor -0.1633 0.3950 -0.414 0.68
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.795 on 206 degrees of freedom
## Multiple R-squared: 0.0008294, Adjusted R-squared: -0.004021
## F-statistic: 0.171 on 1 and 206 DF, p-value: 0.6797
Linear model between the vestibular symptoms cluster score and duration of time to complete RTL protocol. The vestibular coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ vestibular, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2826 -3.1149 -1.2826 0.7174 22.7174
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.2826 0.3775 11.345 <2e-16 ***
## vestibular -0.0129 0.1268 -0.102 0.919
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.797 on 206 degrees of freedom
## Multiple R-squared: 5.028e-05, Adjusted R-squared: -0.004804
## F-statistic: 0.01036 on 1 and 206 DF, p-value: 0.919
Linear model between the sleep symptoms cluster score and duration of time to complete RTL protocol. The sleep coefficient is not significant, suggesting this model is not a good fit.
##
## Call:
## lm(formula = onset_rtl_total_days ~ sleep, data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6926 -2.9701 -1.7651 0.7199 23.0299
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.97012 0.38988 10.183 <2e-16 ***
## sleep 0.13250 0.09277 1.428 0.155
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.773 on 206 degrees of freedom
## Multiple R-squared: 0.009806, Adjusted R-squared: 0.004999
## F-statistic: 2.04 on 1 and 206 DF, p-value: 0.1547
The cognitive symptom cluster appears to be the strongest model and individual symptom cluster predictor of RTL duration; however, no individual model for symptom cluster or total PCSS score is significant to justify a relationship between PCSS symptom severity at the time of ImPACT testing and RTL duration. The lack of a relationship is likely due to the presence of outliers and variance in RTL duration across the sample size.
## predictors delta weight
## 2 cognitive 0.0000000 0.30
## 6 sleep 0.4735140 0.24
## 3 anxiety_mood 0.8650797 0.19
## 1 headache_migraine 2.3706970 0.09
## 4 ocular_motor 2.3506768 0.09
## 5 vestibular 2.5128081 0.09